4:45 – 5:15 pm	Session 18 – Preliminary Reports
Marquis A	The case of an undergraduate mathematics cohort of African American males striving for mathematical excellence Christopher Jett Historically Black Colleges and Universities (HBCUs) provide a different milieu as it pertains to supporting students academically in all disciplines, and this study champions an HBCU effort within the context of undergraduate mathematics. Specifically, it highlights the case of a cohort of 16 African American male mathematics majors at an all-male HBCU. The overarching research question sought to delve deeper into these participantsÕ educational experiences. Using qualitative research methods grounded in critical race theory, preliminary data show that these African American male mathematics majors were affirmed racially and mathematically in their undergraduate mathematics space. Paper 74
Marquis B	Developing an open-ended linear algebra assessment: initial findings from clinical interviews Muhammad Haider, Khalid Bouhjar, Kelly Findley, Ruby Quea and Christine Andrews-Larson The primary goal of this study was to design and validate a conceptual assessment in undergraduate linear algebra course. We work toward this goal by conducting semi-structured clinical interviews with 8 undergraduate students who were currently enrolled or had previously taken linear algebra. We try to identify the variety of ways students reasoned about the items with the intent of identifying ways in which the assessment measured or failed to measure studentsÕ understanding of the intended topics. Students were interviewed while they completed the assessment and interview data was analyzed by using an analytical tool of concept image and concept definition of Tall and Vinner (1981). We identified two themes in studentsÕ reasoning: the first theme involves students reasoning about span in terms of linear combinations of vectors, and the second one involves students struggling to resolve the number of vectors given with the number of entries in each vector. Paper 75
Marquis C	Exploring tensions: LeanneÕs story of supporting pre-service mathematics teachers with learning disabilities Robyn Ruttenberg-Rozen and Ami Mamolo This paper presents a case study of a mathematics teacher educator, Leanne, and her story of trying to support the development of two pre-service elementary school teachers with recognized learning disabilities. We analyze data through a lens of mathematical knowledge for teaching, focusing in particular on concerns and tensions about (i) maintaining academic rigor while meeting the emotional, cognitive and pedagogical needs of her students, (ii) seemingly opposing pedagogies between special education and mathematics education practices, and (iii) equitable opportunities for teachers with disabilities and the consequences for their potential pupils. We offer an analysis of LeanneÕs personal struggle, highlighting implications for teacher education and offering recommendations for future research. Paper 83
Grand Ballroom 5	The Complement of RUME: What's Missing From Our Research? Natasha Speer and Dave Kung The Research in Undergraduate Mathematics Education (RUME) community has generated a substantial literature base on student thinking about ideas in the undergraduate curriculum. However, not all topics in the curriculum have been the object of research. Reasons for this include the relatively young age of RUME work and the fact that research topics are not necessarily driven by the content of the undergraduate curriculum. What topics remain largely untouched? We give a preliminary analysis, with a particular focus on concepts in the standard calculus sequence. Uses for this kind of analysis of the literature base in the education of novice researchers and potential future directions for further analyses are discussed. Paper 86
City Center A	Exploring pre-service teachersÕ mental models of doing math Ben Wescoatt This preliminary study explores the mental models pre-service teachers hold of doing math. Mental models are cognitive structures people use while reasoning about the world. The mental models related to mathematics would influence a teacherÕs pedagogical decisions and thus influence the mental model of mathematics that their students would construct. In this study, pre-service elementary teachers drew images of mathematicians doing math and of themselves doing math. Using comparative judgements, they selected an image that best represented a mathematician doing math. Most images of mathematicians doing math were of a man in front of a blackboard filled with mathematical symbols. The mathematicians appeared happy. In contrast, many images of participants showed them to be unhappy or in confused states. The preliminary results suggest that their shared mental model of doing math is na•ve and shaped by limited experiences with mathematics in the classroom. Paper 90
City Center B	ÔItÕs not an English classÕ: Is correct grammar an important part of mathematical proof writing at the undergraduate level? Kristen Lew and Juan Pablo Mejia-Ramos We studied the genre of mathematical proof writing at the undergraduate level by asking mathematicians and undergraduate students to read seven partial proofs based on student-generated work and to identify and discuss uses of mathematical language that were out of the ordinary with respect to what they considered standard mathematical proof writing. Preliminary results indicate the use of correct grammar is necessary in proof writing, but not always addressed in transition-to-proof courses. Paper 103

Friday